1. Field of the Invention
The present invention is for measuring specular reflectance from a given sample. In particular, it pertains to making absolute measurements with the reflectometer by the use of multiple pass reflections off of the sample. This permits high reflectivity samples to be accurately measured by repeating the number of reflections off the sample a known number of times.
2. Description of the Prior Art
U.S. Pat. No. 3,499,716 to Harold E. Bennett disclosed how to make specular reflections at nearly normal incidence. As was disclosed in the Bennett patent an absolute reflectometer can be made by a variation of a Strong absolute reflectometer as shown in FIG. 1. The strong reflectometer used a flat mirror for mirror 25 whereas the Bennett double reflection technique used a spherical mirror for mirror 25 of FIG. 1 and spherical mirrors 21 and 23 to reflect light off of sample S. The advantage of using spherical mirrors is that a slight sample tilt, as shown by a shift of sample S to position S', permits the deflected light beam to be reimaged to the same position. The use of a spherical mirror 25, having its center of curvature on the sample surface, results in the measurement being insensitive to sample tilt. A plane sample is shown in FIG. 1 and the center of curvature of mirror 25 is halfway between the location of the two beams striking the surface of sample S on the surface of sample S. Tilting the sample causes the light to follow the dotted lines and strike mirror 25 at a different location. However, since a spherical mirror used at its center of curvature returns light to the same point regardless of where it strikes the spherical mirror surface, on second reflection from the flat sample S, the error and tilt is exactly cancelled and the light leaves along the same path whether the sample is tilted or not.
FIG. 2 is a complete light ray path of the Bennett double reflection absolute reflectometer. Mirrors 22, 24, 26, 28, 30, 32, 34, 36, 38, 42, 44, and 46, are plane mirrors. Mirrors 19, 21, 23, 25, 27, 29, 31, 33, and 35 are spherical mirrors. For a detailed breakdown of how the prior Bennett reflectometer functions with regard to FIG. 2, the reader is referred to U.S. Pat. No. 3,499,716 which is herein incorporated by reference. In general, FIG. 2 can be described as comparing measurements with and without sample S for two different configurations. The first is with S as shown and with light reflected to detector D. Next, sample S is removed and the reflection path which is followed for mirrors 30 to 23 to S to 25 to S to 21 to 32 is now altered to have reflection along the path from 30 to 23 to 33 to 21 to 32. While equal path lengths are involved, it is noticed that for comparison purposes that mirrors 33 and 25 have to be either identical or interchangeable. If the sample is rotated 180.degree. and mirrors 30 and 32 are interchanged, the following two measurements occur. Light first follows the dotted path for mirror 32 to 31 to S to 33 to S to 29 to 30 and with the sample removed light travels from 32 to 31 to 25 to 29 to 32. If mirrors 25 and 33 are identical, the ratio of the measurements with the sample in the light path to out of the light path gives the square of the sample reflectance directly. If mirrors 25 and 33 are not identical, they may be effectively interchanged by rotating the sample with mirrors 30 and 32 and measurements taken to obtain a second ratio. If the product of the two ratios is taken, it will give the fourth power of the absolute reflectance and the contribution from the non-identical mirrors cancels. The measurement statistics also improve since twice as many measurements are made as for a single configuration. As described previously, the system is insensitive to sample tilt, the most common source of error in reflectance measurements. The quoted accuracy for the system is .+-.0.1%.
A systematic error will arise in the double reflection system of FIG. 2 if the center of curvature of the spherical mirror is not accurately in the sample surface. The requirement for exact positioning is, from diffraction theory, that the center of curvature not be displaced from the sample surface by more than half the focal range of the mirror. The focal range F is given by F=4.lambda.f.sup.2 where f is the f number of the mirror, the ratio of focal length to the effective diameter of the sample opening for a parallel beam of incident light. .lambda. represents the illuminating wavelength of light. For a f/l system, the requirement is that the center of the mirror coincide with the sample surface to within two wavelengths of light, a difficult requirement. The restrictions ease rapidly as the f number increases.
A simpler, prior art, form of absolute reflectometer is shown in FIG. 3. The reflectometer employs a single sample reflection and a movable detector 50 which swings about an axis 52 through the sample surface to pick up the "sample-in" and "sample-out" beams. The ratio of the two signals then determines the reflectance directly. The disadvantage of this system is that in addition to the requirement for accurately positioning the detector, the reflected beam is reversed left for right on the detector compared to the "straight through" position. Detector non-uniformities significantly limit the accuracy possible using a single reflectance absolute system. If the reflectance of a standard is known accurately, and the position of the sample and standard can be accurately adjusted to coincide, for example, by autocorrelation, the single reflectance technique can give reflectance values with high precision.
An alternate approach for measuring mirror reflectance with precision is to employ a White cell. White cell principles are shown in FIG. 4 for a folded White cell. FIG. 4 shows the principle of the White cell and its folded configuration. Mirrors M.sub.1 and M.sub.3 both have their centers of curvature on the surface of M.sub.2, whose center of curvature is centered between their surfaces. Incoming light is focused at point 0. It is reflected by the sample mirror M.sub.S to M.sub.1 at point 1. The dotted lines represent reflect angular dispersion of the light ray. Mirror M.sub.1 reimages point 0 on the surface of M.sub.2 at point 2. M.sub.2 in turn reflects this light to M.sub.3 at point 3 which reimages the focus again on the surface of M.sub.2 at point 4. Reflection continues to point 5 and point 6 in a similar manner. Reflected light then goes to M.sub.3 at point 7 where it is reimaged at point 8 and falls on a detector. By adjusting the tilt of M.sub.1 and M.sub.3, any odd number of reflections from M.sub.2 can be obtained. For highly reflecting mirrors, hundreds of passes between mirrors are possible. White cells were invented to produce very long path lengths in a gas filling the cell without exceeding the dimensions of the laboratory. They are also useful for obtaining multiple reflections on mirrors without losing light. The key to the performance of the White cell is mirror M.sub.2, which reimages the surfaces of M.sub.1 and M.sub.3, so that none of the light specularly reflected from these mirrors is lost. It thus plays a role similar to that played by mirror 25 in the double bounce reflectometer shown in FIGS. 1 and 2.
Let N=1,3,5 . . . the number of reflections on M.sub.2. Then the number of reflections for mirrors M.sub.1, M.sub.2, and M.sub.3 are 3, 7, 11 . . . 2N+1. There are initially three reflections and they increase by four every time thereafter. The ratio of the flux I emerging from the White cell to that entering it, I.sub.O, is EQU I/I.sub.O =R.sub.1.sup.(N+1)/2 R.sub.2.sup.N R.sub.3.sup.(N+1)/2 R.sub.s.sup.(2N+2)
If we take an average value R for mirrors M.sub.1, M.sub.2, and M.sub.3 and define it by EQU R.sup.4 =R.sub.1 R.sub.2.sup.2 R.sub.3,
the equation for I/I.sub.O can be written EQU I/I.sub.O =R.sub.s.sup.2N+2 R.sup.2N+1 N=1,3,5 . . . ,
where R.sub.s =the reflectivity of the sample mirror and R.sub.1, R.sub.2, and R.sub.3 represent the reflectivity of mirrors M.sub.1, M.sub.2, and M.sub.3 respectively.